Question

Apply the Pythagorean Theorem to find the length between (7'8) (3'2)
. Round your answer to the nearest hundredth

Answer 1

To find the length between the points \( (7, 8) \) and \( (3, 2) \) using the Pythagorean Theorem, we can first calculate the distance between these two points in the coordinate system.

The formula for the distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

In this case, we have:
- \( (x_1, y_1) = (7, 8) \)
- \( (x_2, y_2) = (3, 2) \)

Now we can substitute the values into the formula:

1. Calculate \( x_2 - x_1 \) and \( y_2 - y_1 \):
\[
x_2 - x_1 = 3 - 7 = -4
\]
\[
y_2 - y_1 = 2 - 8 = -6
\]

2. Now square these differences:
\[
(x_2 - x_1)^2 = (-4)^2 = 16
\]
\[
(y_2 - y_1)^2 = (-6)^2 = 36
\]

3. Add the squares:
\[
(x_2 - x_1)^2 + (y_2 - y_1)^2 = 16 + 36 = 52
\]

4. Finally, take the square root to find the distance:
\[
d = \sqrt{52} \approx 7.2111
\]

Rounding this to the nearest hundredth:
\[
d \approx 7.21
\]

Thus, the length between the points \( (7, 8) \) and \( (3, 2) \) is approximately **7.21**.